The PostgreSQL Global Development Group provides
the PostgreSQL software code tree as a public service,
without warranty and without liability for its behavior or performance.
However, at the time of writing:

The author of this statement, a volunteer on the
PostgreSQL
support team since November, 1996, is not aware of
any problems in the PostgreSQL code base related
to time transitions around Jan 1, 2000 (Y2K).

The author of this statement is not aware of any reports of Y2K problems
uncovered in regression testing
or in other field use of recent or current versions
of PostgreSQL. We might have expected
to hear about problems if they existed, given the installed base and
the active participation of users on the support mailing lists.

To the best of the author's knowledge, the
assumptions PostgreSQL
makes about dates specified with a two-digit year
are documented in the current User's Guide
in the chapter on data types.
For two-digit years, the significant transition year is 1970, not 2000;
e.g. 70-01-01 is interpreted as 1970-01-01,
whereas 69-01-01 is interpreted as 2069-01-01.

Any Y2K problems in the underlying OS related to obtaining the
"current time" may propagate into apparent Y2K problems in
PostgreSQL.